enable comparison of tight binding and parabolic dispersion
– to compare the transfer matrix method – which has a truly parabolic dispersion, and the tight binding method, which has a cosine dispersion, we should build in a display mechanism to compare the relevant dispersions. The lowest energy material (typically the well) should have only a propagating (positive k) dispersion. Any other material (barrier and well) that has a higher energy level (conduction band) should show a positive propagating dispersion (positive k) for energies above the conduction band edge. These materials should also have an attenuating “kappa” towards the negative “k” axis that will indicate the attenuation in the barriers for energies below the conduction band. I would like to be able to experiment with the cosine dispersion of the tight binding, when I modify the lattice constant and effective mass. A very heavy mass or a lattice constant that is too large will make the cosine dispersion deviate rapidly from the parabolic dispersion and cause interesting effects in the overall structure.